Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	53×	body	1280	valid
12.0ms	49×	body	640	valid
9.0ms	149×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.1b	(/ 1.0 (sin B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

8.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (tan B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* x (/ 1.0 (tan B)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (tan B))
18.0ms	(/ 1.0 (sin B))
105.0ms	(* x (/ 1.0 (tan B)))

simplify49.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604

prune308.0ms

Filtered

115 candidates to 90 candidates (78.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	8	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ 1.0 (sin B))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

15.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ (* x 1.0) (tan B))
3.0ms	(/ 1.0 (sin B))

series237.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
110.0ms	(/ (* x 1.0) (tan B))
19.0ms	(/ 1.0 (sin B))

simplify38.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	336	465
1	1303	419
2	5001	414

prune188.0ms

Filtered

74 candidates to 55 candidates (74.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Merged error: 0.0b

Counts

82 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b	(/ (tan B) (* x 1.0))
0.1b	(/ 1.0 (sin B))
0.4b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 123

Calls

4 calls:

34.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
5.0ms	(/ (tan B) (* x 1.0))
3.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
48.0ms	(/ (tan B) (* x 1.0))
20.0ms	(/ 1.0 (sin B))
83.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	531	922
1	2284	808
2	5002	756

prune289.0ms

Filtered

135 candidates to 85 candidates (63.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Merged error: 0.0b

Counts

142 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (tan B) (* x 1.0))) (cbrt (/ (tan B) (* x 1.0))))
0.8b	(cbrt (/ (tan B) (* x 1.0)))
0.8b	(cbrt (/ (tan B) (* x 1.0)))
0.8b	(cbrt (/ (tan B) (* x 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

9.0ms	(* (cbrt (/ (tan B) (* x 1.0))) (cbrt (/ (tan B) (* x 1.0))))
3.0ms	(cbrt (/ (tan B) (* x 1.0)))
3.0ms	(cbrt (/ (tan B) (* x 1.0)))
3.0ms	(cbrt (/ (tan B) (* x 1.0)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt (/ (tan B) (* x 1.0))) (cbrt (/ (tan B) (* x 1.0))))
156.0ms	(cbrt (/ (tan B) (* x 1.0)))
157.0ms	(cbrt (/ (tan B) (* x 1.0)))
154.0ms	(cbrt (/ (tan B) (* x 1.0)))

simplify122.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	277	1097
1	923	1022
2	4489	926
3	5001	917

prune416.0ms

Filtered

115 candidates to 93 candidates (80.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	115	8	123

Merged error: 0.0b

Counts

123 → 8

regimes64.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

704.0ms	1683×	body	1280	valid
373.0ms	1394×	body	640	valid
291.0ms	4955×	body	80	valid
130.0ms	701×	body	320	valid
51.0ms	369×	body	160	valid